Structures for M-channel perfect-reconstruction FIR QMF banks which yield linear-phase analysis filters

The authors develop structures for FIR (finite impulse response) perfect-reconstruction QMF (quadrature mirror filter) banks, which cover a subclass of systems that yield linear-phase analysis filters for arbitrary M. The parameters of these structures can be optimized to design analysis filters with minimum stopband energy which at the same time have linear phase and satisfy the perfect-reconstruction property. If there are M subbands, then depending on whether the coefficients h_k(n) of each analysis filter are symmetric or antisymmetric, several combinations of filter banks are possible. Some of these permit perfect reconstruction and some do not. For a given M, the authors develop a formula for the number of combinations for a subclass of linear-phase perfect-reconstruction structures. As an example, they elaborate on a perfect-reconstruction linear-phase lattice structure for three channels. The lattice structure is such that, regardless of the parameter values, the QMF bank enjoys the perfect-reconstruction property while at the same time the analysis filters have linear phase. A design example is presented, along with tables of impulse response coefficients